Regularity in parabolic systems with continuous coefficients

Under the only assumption of continuous coefficients, we prove a partial H?lder continuity result for solutions to parabolic systems with polynomial growth. A key component throughout the argument is the use of DiBenedetto’s intrinsic geometry (Degenerate Parabolic Equations. Universitext. Springer, New York, 1993) to accommodate the inhomogeneity in the system. A main technical point is that, although we are proving the H?lder continuity of solutions, we employ the intrinsic geometry using cylinder stretched according to the size of the (spatial) gradient, in an iteration scheme that does not necessarily imply the boundedness of the gradient itself.     

Organocatalytic Dakin oxidation by nucleophilic flavin catalysts

Flavin catalysts perform the first organocatalytic Dakin oxidation of electron-rich arylaldehydes to phenols under mild, basic conditions. Catechols are readily prepared, and the oxidation of 2-hydroxyacetophenone was achieved. Aerobic oxidation is displayed in the presence of Zn(0) as a reducing agent. This reactivity broadens the scope of biomimetic flavin catalysis in the realm of nucleophilic oxidations, providing a framework for mechanistic investigations for related oxidations, such as the Baeyer-Villiger oxidation and Weitz-Scheffer epoxidation.     

On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some γ > 0 to a subclass of the class S _γ (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the “spatially local” asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds.     

Two ergodicity criteria for stochastically recursive sequences

We prove two criteria for so-called coupling- and strong coupling-convergence of stochastically recursive sequences.     

Nanoscale topography reduces fibroblast growth, focal adhesion size and migration-related gene expression on platinum surfaces

Controlling cellular responses on biomaterial surfaces is crucial in biomedical applications such as tissue engineering and implantable prosthetics. Since cells encounter various nanoscale topographic features in their natural environment, it has been postulated that surface nanotopography may be an alternative route to fabricate biomaterials with a desirable cellular response. In this framework, we investigated the responses of primary human fibroblasts to platinum substrates with different levels of surface roughness at the nanoscale. The nanorough surfaces were fabricated by using the glancing angle deposition technique (GLAD). We found that levels of cellular responses depended on the surface roughness and the size of the nanoscale features. We showed that in response to nanotopography cells spread less and have an elongated morphology, displaying signs of actin cytoskeleton impairment and reduced formation of focal adhesion complexes. Although cell growth and adhesion were impaired on the nanorough substrates, cell viability was not affected by topography. To a minor extent our results also indicate that cell migration might be reduced on the nanorough surfaces, since a significantly lower gene expression of migration related genes were found on the roughest surfaces as compared to the flat reference. The results presented here demonstrate that surface nanotopography influences fibroblasts responses on platinum, which may be used to reduce cellular adhesion on platinum implant surfaces such as implantable neural electrodes.     

Design of polarization-maintaining retro-reflector for folded-path applications

A design of polarization-maintaining retro-reflectors(PMRRs) for folded-path applications is proposed and analyzed.The prism-based scheme enables the output light,which is parallel to the input,to have an identical state of polarization.The principle of the design is theoretically verified,and the related error is analyzed due to possible manufacturing imperfection.The maximum spatial angle error is ±2.75°.The effect on the extinction ratio and insertion loss is also discussed,which further proves the design’s feasibility in practical applications.     

Attributes of the large-scale coherent motions in a shear layer

PIV observations in a shear layer have been used to identify and characterize the discrete large-scale coherent motions (LSCMs) in the nominally self-preserving region: x/θ_o ≈ 450–610, of a shear layer. The LSCMs are given an objective definition wherein their centers are the (swirling flow pattern) nodes of the velocity-vector field as seen by an observer in the Galilean reference frame translating at an appropriately defined reference velocity. The statistical attributes of size, lateral location, and separation between these coherent motions (that exist in a single image) as well as their characteristic vorticity magnitude 〈ω_max〉 are reported.